The Lesson
A tree diagram shows all the possible outcomes of an event and their probabilities. We can find the probability of one event or another event.A Single Coin Toss
A single coin toss can be shown on a tree diagram.The probability of each event can be read from each branch:
- The probability of getting Heads is ^{1}⁄_{2}.
- The probability of getting Tails is ^{1}⁄_{2}.
The probability of Heads or Tails is found by adding their probabilities.
^{1}⁄_{2} + ^{1}⁄_{2} = 1
How to Find the Probability of an Event or Another Event on a Tree Diagram
The addition rule can be used for more complicated tree diagrams. The tree diagram below is for a double coin toss.Question
What is the probability of both tosses landing the same side up?Step-by-Step:
1
Find the event given in the question.
The event is the coin landing the same side up on both tosses. There are two ways this can happen:
- Heads and Heads
- Tails and Tails
2
Use the multiplication rule to find the probabilities of the outcomes.
Multiply the probabilities along the branches.
For Heads and Heads:
For Heads and Heads:
P(Heads and Heads) = ^{1}⁄_{2} × ^{1}⁄_{2} = ^{1}⁄_{4}
For Tails and Tails:
P(Tails and Tails) = ^{1}⁄_{2} × ^{1}⁄_{2} = ^{1}⁄_{4}
3
Add the probabilities for these outcomes.
^{1}⁄_{4} × ^{1}⁄_{4} = ^{2}⁄_{4}
4
Simplify the fraction if possible. (The fraction in our example is already as simple as possible).
Simplify the fraction by dividing the top and bottom numbers by their greatest common factor (which is 2).
2 ÷ 2 = 1
4 ÷ 2 = 2